\[ (a_{n+1})^{2}a_n + 2(a_{n+1})-a_n=0\]

Let a recursive sequence \( \{a_n\}\) be defined as given above with \(a_0=1\), then evaluate \[ \lim_{n \rightarrow \infty} \left [ 2^{n}(a_n) \right ] \]

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